Valuing companies and investment projects

Valuing companies and investment projects tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả...

TOPICS

Basic Ideas

Compounding/Terminal Value

Discounted Present Value DPV \ Discounted Cash Flow DCF

Investment ( Project) Appraisal, Internal Rate Of Return,

Valuation Of The Firm: Enterprise Vale and Equity

~ choice of discount rate

~ valuation in practice: EBITD, Depreciation, FCF etc.

Complementary Valuation Techniques: EP, EVA,APV

Investments:Spot and Derivative Markets, K.Cuthbertson

and D.Nitzsche

Chapter 3

Discounted Present Value DPV \ Discounted Cash Flow DCF

Internal Rate Of Return, IRR

Investment ( Project) Appraisal

Valuation Of The Firm And The Firm’s Equity (Incl Continuing Value).

Valuation In Practice: EBITD, Depreciaiton, FCF etc

Other Investment Appraisal Methods

Chapter 11

Economic Profit, Economic Value Added, Adjusted Present Value

P 342-346.

BASIC IDEAS

Compounding/Terminal Value

Discounted Present Value DPV

Discounted Cash Flow DCF

Internal Rate of Return

Investment/ Project Appraisal

Compounding/ Terminal Value

Assume zero inflation+cash flows known with certainty

Vo = value today ($1000), r = interest rate (0.10)

Value in 1,2 years time

V1 = (1.1) 1000 = $1100

V2 = (1.1) 1100 = (1.1) 2 1000 = $1210

Terminal Value after n-years: Vn = Ao (1 + r) n

We could ‘move all payments forward’ to time n=10 years and

then add them - but we do not do this

‘Bring all payments back’ to t=0 and then add.

Value today of V2 = $1210 payable in 2 yrs ?

2

1

1210 11

1

( + r)

Discounted Present Value (DPV)

What is value today of stream of payments - usually

called ‘Cash Flows’, assuming a constant discount

factor? :

DPV = = d1 V1 + d2 V2 +

r = ‘discount rate’

d = “discount factor” < 1

Discounting, puts all future cash flows on to a ‘common

time’ at t=0 - so they can then be “added up”

V r

V r

2

( + ) ( + + ) +

Operating Cash Flows, (ie revenues less operating costs, less

taxes) V1 = $1100, and V2 = $1210

Then DPV(of ‘cash flows’ at r =10%) = $2000

Suppose Capital Cost (Investment Expenditure), KC = $2000

Net Present Value (NPV): NPV = DPV - KC

RULE: If DPV > KC then invest in project

OR If NPV > 0 then invest in project

Investment (Project) Appraisal:Decision Criteria

NPV

r= loan rate

or discount rate

Businessmen think in terms the rate of return on the project

What is the rate of return (on capital investment of

$2000) ?

It is the rate of return which gives NPV = 0

Hence the IRR is the ‘break-even’ discount rate and IRR = 0.10

(10%)

IRR INVESTMENT DECISION RULE

Internal Rate Of Return (IRR)

0

2000 )

1 (

1210 )

1 (

1100

+ +

If NPV = 0

OR, IRR = cost of borrowing then this

implies

-the CF from the project will just pay of

a ll the annual interest payments on the loan + the principal amount borrowed

from the bank

Note: Internal funds are not ‘free’

Intuitively what do NPV and IRR rules mean ?

Valuation of the Firm:

Enterprise Value and Equity Value

General Case

V0 = FCF1 / (1+r) + FCF2 / ((1+r)2 + ……

FCF= Free Cash Flows

1) Sum to infinity and FCF is constant:

Enterprise DCF

In practice investment costs occur every year so:

V(whole firm) = DPV ( Free Cash Flows, FCF)

FCF = (Operating ‘cash flows’ - Gross investment)

FCF = (Operating ‘cash flows’ - Gross investment) each year

Value of Equity

V(Equity) = V(whole firm) - V(Debt outstanding)

‘Fair value for one share’ = V(Equity) / N

N = no of shares outstanding (+ ‘minority interests’)

‘Enterprise Value’ and ‘Equity Value’

In an efficient market the price of the

share(s) should equal ‘fair value’

We will learn how to value corporate

debt, in later lectures

‘ Enterprise Value’ and Equity Value

The DPV of ALL the firm’s future cash flows is

often ‘split’ into two (or more) planning horizons:

‘ENTERPRISE DCF’

= DPV of FCF in years 1-5 + DPV of ‘Continuing Value’ after year-5

‘Valuing the ‘Firm’ :Continuing Value

Special Case A:

i) the discount rate is constant in each year

ii) Cash flows, FCF are constant in each year and persist

‘for ever’ (ie perpetuity) then

CV = FCF/ r

This is often used to calculate ‘continuing value’, CV

‘ Valuing the ‘Firm’ :Continuing Value

eg Project has

Continuing value CV (at t=5) = 100 / 0.10 = 1,000

and

DPV (at t=0) of the CV = 1000/ (1+r)5 = 621

‘ Valuing the ‘Firm’ :Continuing Value

Special Case B:

If

i) the discount rate is constant in each year

and

ii)FCF’s grow at a constant rate each year, say

after year-5 then

CV (at t=5) = FCF5 (1+g) / ( r - g) for r>g

‘Valuing the ‘Firm’ :Continuing Value

Project has FCF=100 in year-5

FCF grows at rate g=0.03 (3%) and r = 0.10

CV is very sensitive to the choices made for FCF5, R and g.

CV can be a large & dominates DPV of the cash flows over years 1-5.

‘ Valuing the ‘Firm’ :Continuing Value

Value of firm using DPV of FCF’s is

Enterprise DCF = DPV (FCF 1-5yrs) + DPV (of CV)

= 679 + 621 = 1,300

Suppose: All equity financed firm N = 1000 shares and P= $1

Market Value (Capitalisation) = $1000

Hence the shares are undervalued by 30%

Company Valuation: M&A

If NPV of the project > 0 (discounted using RS)

(which exceeds the return they could earn from investing their money in other hamburger firms)

value’

Shareholder Value (All equity financed firm)

Choice of Discount Rate

Note: ‘All equity’ financed = ‘unlevered firm’ - ie no debt

Discount rate should reflect ‘business risk’ of the project

Assume project is ‘scale enhancing’ (eg more hamburger outlets for McDonalds)

Hence, has same ‘business risk’ as the firm as a whole.

Simple method

Use the average (historic) return on equity, RS (e.g 15%) for this (hamburger) firm as the discount rate

This assumes the observed return on equity correctly reflects

the payment for risk , that shareholders require from this

hamburger company.

Discount Rate: All equity financed firm

If the project being considered by MacDonalds is to build

hotels, then we would use the average stock market

return in “hotel sector” (20%pa say)

- as this reflects the “required return on equity capital” for

the shareholders in that sector

- see CAPM / SML / APT later, where we provide more

sophisticated methods for choosing the appropriate equity discount rate

Discount Rate: All equity financed firm

Levered firm = financed by mix of debt and equity

Assume debt-equity ratio will remain broadly unchanged after

the new project is completed.

Then discount FCF using:

(‘After tax’)Weighted Average Cost of Capital WACC,

S = market value of outstanding equity ( = N x stock price)

B = market value of outstanding debt (ie bonds issued and

bank loans)

RS = average return on equity in hamburger industry

RB = interest rate (yield to maturity) on say 10-year corp

AA-rated bonds(If hamburger company is AA-rated AA by S&Poor’s)

t = corporate tax rate

Note: Market value (‘cap’) of the firm V = S +B

Discount Rate: levered firm

Assume firm is part-equity financed and part-debt financed

Then the ‘intrinsic value’ of the firm is the DPV of its future

cash flows from all of its current and future investment

projects, discounted using WACC

Managers can only increase the value of the firm by

1) investing in projects with ‘high’ FCFs

2) reducing the WACC

‘(2)’ is the so-called capital structure question - can

managers change the mix of debt and equity financing to lower the overall WACC? - assuming FCF is

unchanged - see Modigliani-Miller later

Can Managers Increase the Value of the Firm?

1) Key practical method is to use “sensitivity” or “scenario”

analysis.

Sensitivity - ‘one at a time’

1) What is NPV if revenues are much higher/lower ?

2) What is the NPV if the discount rate is 1% higher?

Scenario:

3) What is the NPV if both (1) and (2) apply - scenario analysis (Monte Carlo simulation is a sophisticated way of doing this)

Can “include” probabilities in (1) and hence calculate

EXPECTED NPV and its standard deviation.

What about (business) risk in DCF ?

2) Can use decision trees - particularly useful where there

are strategic options in the investment decision

for $10m if demand turns out to be ‘low’ in year-2 On the other hand if demand is ‘high’ then you will continue

production in year-2

This affects the NPV of the project compared with the

‘normal case’ where you assume you do not abandon

In fact the ‘correct’ way to evaluate these strategic options is

cannot be done here !

What about (business) risk in DCF ?

VALUATION IN PRACTICE:

EBITD, DEPRECIAITON, FCF

ACCOUNTING NIGHTMARES Earnings before interest, tax and depreciation,EBITD

EBITD

= R - C = Sales Revenues - Operating Costs (Labour+Materials)

Free Cash Flow FCF

= (R - C - T) - Inv(gross) - Increase in WC + (Net Non-Op Inc)

Valuing a Company: ‘Cash is King’

Calculating ‘Free Cash Flow’ in Practice

Now the Accountants ‘Mess it About’

Published ‘Earnings’ or ‘profit’ are usually presented after a

deduction for depreciation: These would be ‘earnings before

interest and tax’ EBIT

So, EBIT = EBITD - D = (R-C) - D

Hence, to get FCF ‘add back’ depreciation and deduct taxes:

FCF =(EBIT - T) + D - Inv(gross) - Increase in WC +(N.N.Op.Inc) Also, you often ‘see’ (in the UK):

Valuing a Company: ‘Cash is King’

Notes: 1 Total capital cost is KC = $1,000 Scrap value SV = 0 at n=5 years.

Hence D = (KC – SV)/5 = 200 per year (straight line depreciation).

2 ( ) indicates a negative number

Valuing a Company

Table 3.8 : DEPRECIATION AND TAX

1

2

3

4

5

ote : 1 EBITD = earnings before interest, tax and depreciation Accounting profits (before tax)

reported in the ‘income-expenditure’ (or ‘profit-loss’) account would be (EBITD – D).

Table 3.9 : CALCULATING FREE CASH FLOW

Tax and Depreciation,

2 An increase in working capital is a cash outflow Figures are from table 3.7 (row 7).

3 These are the actual cash expenditures on investment in each year and they sum to the total capital cost KC (in table 3.7).

and 10.

Valuing a Company

Table 3.10 : USE OF FREE CASH FLOW OF THE FIRM

1

2

3

4

5

Year-1 Free Cash Flow

(table 3.9, row 12)

-600 -15 560 990 1,200

FINANCING (USE OF FREE CASH FLOWS)

Complementary Valuation Techniques:

Economic Profit, EP Economic Value Added, EVA Adjusted Present Value, APV

EP and EVA are equivalent to ‘Enterprise DCF’ if the calculations are done consistently -ie before the accountants get at the figures ECONOMIC PROFIT (McKinsey and Co)

EP = ( ROC - WACC) x Capital Stock, K where Return on Capital, ROC = ‘Profit’ / K

If ROC > WACC then the managers chosen investment projects are earning a rate of return in excess of WACC and therefore, the investment projects are ‘Adding value’.

Economic Profit

ECONOMIC PROFIT (Example)

Profit = 150, K = 1000 hence ROC = 15% p.a

Let WACC = 10% p.a.

EP = (15% - 10%) 1000 = $50 p.a

Your current stock of capital is being used in such a way as to

generate $50 p.a even after allowing for an annual ‘dollar capital charge’ of $100 p.a.

Economic Profit

EVA= ‘Profit’ - ‘Capital Charge’ = 150 - (10%)1000 = $50 p.a.

where ‘Capital charge’ = WACC x ‘Adjusted Capital’, K

EVA is equivalent to EP if we measure ‘profit’ and ‘capital’ in the same way, for both techniques

eg do we ‘add back’ to ‘capital’ past R&D expenditures on the grounds that this outlay increased ‘knowledge’ which is an

Economic Value Added, EVA

You can compare different firms’ performance on EP and EVA

in any one year (or over several years)

The ‘plus’, compared to using say just ‘profits’ or ROC is that

EP and EVA assess ‘profit’ in relation to ‘the cost of capital’.Value of the firm (at t=0 ) using EP or EVA

+ DPV ( of EP or EVA p.a., ~ WACC as discount rate)

EP and EVA

Simple proof that ‘Enterprise DCF’ and EP or EVA are equivalent:

EVA Capital,K ROC WACC

General Motors -3527 94,268 5.9 9.7 Johnson & Johnson 1327 15,603

A positive return on capital of 5.9% for GM is ‘not enough’ if you have a WACC of 9.7%

- it results in a negative EVA (or EP)

Source: Fortune Mag 10th Nov 97.

Complementary Valuation Techniques:

ROC, EVA and EP

When using ‘Enterprise DCF’ we discounted the FCF using ‘after tax’ WACC

Our measure of FCF did not contain any ’tax offsets/shields’ on (debt) interest payments (the only tax offsets we considered were on

depreciation).

This was because these ‘tax offsets’ are taken care of in the

denominator, the WACC, which is reduces the cost of debt to R b (1-t).

APV and Enterprise DCF give the same value for the firm if consistent measures of the cost of equity and debt are used This is a difficult area which we cannot pursue here but note that

APV = FCF discounted as if firm is all-equity + DPV of ‘tax offsets’

Adjusted Present Value, APV(Not Examinable)

END OF LECTURE SELF STUDY SLIDES FOLLOW

1) SOME PATHOLOGICAL CASES

~ COMPLICATIONS WITH IRR !

2) OTHER METHODS USED IN

INVESTMENT APPRAISAL

(These are of minor importance but you

should be aware of these issues)

SELF STUDY

Table 2: ‘DIFFERENT CASH FLOW PROFILES

Project B ~ ‘Rolling Stone’s Concert’

Project C ~ ‘Open cast mining’

-IRR gives wrong decision for B and C

NPV gives correct decision for A,B,C

ANSWER: Use NPV !

Complications: Mainly with IRR !

Mutually exclusive projects

(eg garage or hamburger joint on one site, BUT NOT

BOTH)

- use NPV not IRR criterion

(afficionados could use the incremental-IRR criterion ! )

Capital Constraint

(ie not enough funds for all projects with NPV>0)

- rank projects by the ‘profitability index’, PI where:

PI = ( NPV / Capital Cost) = “bang per buck”

Choose those projects with largest PI values until you

Complications: Mainly with IRR !

Year-0 Year-1 Year-2 Year-3 Year-4

FV -1000 500 500 700 0

d 1.0 0.8696 0.7561 0.4972

PV 1000 435 378 348 Note: NPV = 161

-1) Payback Period = 2 years

2) Discounted Payback = 2-3 years

Investment Appraisal: Alternative Methods

Ignores cash flows after payback period

(eg never invest in ‘Dolly the sheep’)

OR

Ignores time value of money

Deficiencies: Alternative Methods

END OF SLIDES